Nick Clegg has said part of the reason he has taken such a strong stance on Syria, by supporting military strikes after the chemical weapons attack, was that his family had been "disfigured" by wars in the last century.

The deputy prime minister, who was speaking on his weekly LBC Radio phone-in programme, also suggested that Ed Miliband was not acting in the national interest when he defeated a government motion on Syria.

The deputy prime minister told LBC: "I am not going to hide my own personal view as a committed internationalist. It is also partly where I come from. My whole family, like lots of families, was disfigured by the terrible violence and abuses of [the last century]. My dad's mum fled from revolutionary Russia, my mum spent a large part of her childhood in a prisoner of war camp.

"It is partly about where you come from as a person as well as what your political views are. I just think sometimes you have to do the uncomfortable thing which is to say: 'No, a line has been crossed. This cannot go without consequences.'"

Clegg, who faced a major rebellion among Liberal Democrat MPs during last week's Commons vote, said he understood and respected people who took a different view. But he was highly critical of Miliband after the Labour leader forced a division in the Commons after the government had addressed his concerns in its motion.

Clegg said: "What was frustrating was that we had bent over backwards to address all the concerns that he and Douglas Alexander had raised in meetings with me and David Cameron. We changed our motion constantly. Even right up to the last minute we changed it to accept a succession of suggestions they had made.

"And then you had this rather odd situation at the end where we had said we are genuinely trying to be consensual – because it is in everybody's interests that we don't make this a party political point-scoring issue – we have accepted all your suggestions. And then they came up with a rival motion to divide the house, rather than unite it, even though the motions were to all intents and purposes the same.

"And that's when I just really thought: well hang on a minute, surely we can just rise to the occasion and try and try and not create rival motions which say almost exactly the same thing but instead try and act in the national and international interest."